Skip to main content

What Is a Catenary Curve and How Do We Build One in FreeCAD?

The catenary curve (also known as a chainette) comes from the Latin word catenaria, meaning “chain.” This type of curve naturally occurs when a uniform flexible material, like a rope, chain, or cable, hangs freely under its own weight between two supports.

In everyday life and engineering, the catenary shape appears in:

  • Hanging chains

  • Overhead cables

  • Suspension elements

  • Spider webs and vines in nature

It distributes weight evenly between its two ends, forming a mathematically predictable and stable arc.

The Challenge: Modeling a Catenary in FreeCAD

At the time of writing, FreeCAD does not provide a built-in tool to generate a catenary curve with a single click. The only earlier implementation came via the now-discontinued Animation Workbench, where animation paths were used as geometry.

My goal is to explore how we might generate a catenary using FreeCAD's Curves Workbench by plotting a set of points and applying interpolation or approximation techniques to build the curve. Once created, the curve could then serve as a path in other workbenches like Draft or Lattice2, ideal for object arrays or structural modeling.

If anyone has an existing solution for this, please let me know, I’d be happy to add a reference or link here.

R&D: Simplifying the Problem

To approach this, I’ve broken the challenge into manageable steps.

Phase 1 – Proof of Concept

  1. Manually create 2D points (using Draft or Sketch workbench) and test with the Curves Workbench to see if a valid path can be generated.

  2. Repeat this process using a Python script to generate the same point set.

  3. Research and find an equation to compute catenary coordinates. As this is a classical math problem, resources in other programming languages are available and can be adapted.

  4. Integrate the equation into a FreeCAD macro to automate the plotting of the curve.

Phase 2 – Refinement and Expansion

Once the 2D version is proven to work:

  • How can this be expanded into 3D space?

  • What happens if one support is higher than the other?

  • How do different support distances affect the curve’s depth?

These are questions I hope to explore in future updates.

Resources and References

Here are some excellent starting points for understanding and coding the catenary curve:

These will be invaluable as I translate the logic into FreeCAD-compatible Python code.

Final Thoughts

Modeling a catenary curve in FreeCAD is both a mathematical and practical challenge. With the help of scripting, community resources, and FreeCAD’s flexible architecture, it’s entirely possible to create accurate and usable versions of these natural shapes.

If you're experimenting with structural curves, cables, or even artistic elements in FreeCAD, this could open up a range of creative possibilities.

Stay tuned for the macro and future updates, and if you’re working on something similar, feel free to connect.


Comments

Popular posts from this blog

Beginners FreeCAD: Exercise 5.1 & 5.2 (Reference Images)

Welcome to the total beginners course to FreeCAD 0.20. In this is a two part lesson we will practice our tracing skill in the form of a mini project. Using the below reference photos we will create a more complex part which will consist of repeating features. We will utilise the symmetry tools to ease construction in both FreeCAD sketcher and Part Design workbench. This project work will help teach the fundamentals of freeCAD allowing a understanding of the basics but delivering this information via teaching you different workflows. In this tutorial we will be tracing photos imported into FreeCAD via the image workbench https://wiki.freecadweb.org/Image_Workbench JUMP TO IMAGES Do you want to purchase the complete series along with others and keep forever?  Check out my shop https://ko-fi.com/mang0/shop The story of this tutorial The idea and first attempt at creating this tutorial was back in FreeCAD 0.18.  The physical part itself, well, I have no idea what really it is, i...

FreeCAD For Beginners: CAD Thinking Part 1

Step-by-Step CAD Thinking FreeCAD Tutorial: Modeling a Latch Part (Part 1) Learning how to turn real life objects into CAD Models. Using FreeCAD we explain at a beginner level how to break down a physical object into its primitive shapes to digitise it into a 3D model, with this episode we are looking at a multi-part assembly, modelling each piece individually. The series aims to open your eyes and mind giving you the ground skills to pick the correct profiles, geometry and workflow when it comes to modelling your parts. This is not just for FreeCAD but for all CAD packages out there. Introduction This tutorial is the first in a series guiding you through modeling a latch assembly in FreeCAD (version 0.21) using the Part Design and A2Plus workbenches. It focuses on modeling the first part (a slotted component) by selecting the top profile to create a slot and adding side arcs, emphasizing CAD thinking to break down complex shapes into primitives. The tutorial highlights model stability...

Beginner FreeCAD Tutorial 14: Reference Document for Exercise 1

This tutorial focuses on modelling a deck eye plate. These items are normally made of stainless steel with some kind of galvanised coating to stop corrosion. They are used in many industries but are most commonly found around boats, ships, sail lofts and docks where they play an important part in marine industry. Finding their use in many applications, they are often wall mounted acting as lashing points for mooring and for tying down sails or canopies. They can even be used for domestic use around the house and garden, for example to anchor ropes, cords and lines. So if your into 3D printing your finished creations, you can make use of the finished result.   Disclaimer : The strength of the part will depend on the internal structure, settings of the slicer and the material it has been printed on.  This will limit its application as failure of the part, damage to property and injury is a possibility.  These items are normally made of steel and are tested to take a...